A method to achieve High-Brightness Self-Amplified Spontaneous Emission (HB-SASE) in the Free Electron Laser (FEL) is described. The method uses repeated non-equal electron beam delays to de-localise the collective FEL interaction and break the radiation coherence length dependence on the FEL cooperation length. The method requires no external seeding or photon optics and so is applicable at any wavelength or repetition rate. It is demonstrated using linear theory and numerical simulations that the radiation coherence length can be increased by approximately two orders of magnitude over SASE with a corresponding increase in spectral brightness. Examples are shown of HB-SASE generating transform-limited FEL pulses in the soft X-ray and near transform-limited pulses in the hard X-ray. Such pulses may greatly benefit existing applications and may also open up new areas of scientific research.In the X-Ray region of the spectrum Self-Amplified Spontaneous Emission (SASE) free-electron lasers (FELs) are currently opening up new frontiers across science [1][2][3][4][5][6]. Although SASE FELs have brightness up to 10 8 times greater than laboratory sources their full potential is limited by a relatively poor temporal coherence. In this Letter, a High Brightness SASE (HB-SASE) FEL is described which may significantly improve the temporal coherence towards the transform limit, enhancing the spectral brightness and potentially enabling X-ray FELs to enhance their existing scientific capability and to access new experimental regimes.Applications that may benefit include Resonant Inelastic X-ray Scattering (RIXS) [7] which requires substantial incident photon flux to collect sufficient spectra with a high enough resolution in energy and momentum in a reasonable time. RIXS has evolved greatly over the last decades, due to increases in photon flux from synchrotron sources then X-ray FELs, as well as advances in instrumentation. Each increase in resolution has revealed new details in material excitation spectra. Further improvement may extend study to e.g. single magnons in small exchange systems and the full dispersion curves of superconducting gaps. New applications made possible by fourier-transform limited X-ray pulses may include time-resolved X-ray spectroscopy of chemical dynamics, or quantitative studies of molecular and cluster fragmentation, where high repetition rate pulses of controlled temporal profile are essential for systematic studies of nonlinear phenomena [8].In the SASE FEL [9, 10], a relativistic bunch of electrons with a Lorentz factor of γ ≫ 1 enters an undulator comprising an array of transverse, alternating polarity dipole magnets of period λ u . The undulator magnetic fields cause the electrons to oscillate transversely and emit initially incoherent radiation. A cooperative (or collective) instability in the coupled electron-radiation system may cause an exponential gain in the radiation field and an electron microbuncing at the resonant radiation wavelength λ r = λ u (1 +ā2 , whereā u is the rms undul...